Question: Simplify the following expression: $\dfrac{60y}{50y^3}$ You can assume $y \neq 0$.
Solution: $ \dfrac{60y}{50y^3} = \dfrac{60}{50} \cdot \dfrac{y}{y^3} $ To simplify $\frac{60}{50}$ , find the greatest common factor (GCD) of $60$ and $50$ $60 = 2 \cdot 2 \cdot 3 \cdot 5$ $50 = 2 \cdot 5 \cdot 5$ $ \mbox{GCD}(60, 50) = 2 \cdot 5 = 10 $ $ \dfrac{60}{50} \cdot \dfrac{y}{y^3} = \dfrac{10 \cdot 6}{10 \cdot 5} \cdot \dfrac{y}{y^3} $ $\phantom{ \dfrac{60}{50} \cdot \dfrac{1}{3}} = \dfrac{6}{5} \cdot \dfrac{y}{y^3} $ $ \dfrac{y}{y^3} = \dfrac{y}{y \cdot y \cdot y} = \dfrac{1}{y^2} $ $ \dfrac{6}{5} \cdot \dfrac{1}{y^2} = \dfrac{6}{5y^2} $